A285768 Moebius transform of repunits (A002275).

1, 10, 110, 1100, 11110, 110990, 1111110, 11110000, 111111000, 1111099990, 11111111110, 111110998900, 1111111111110, 11111109999990, 111111111099890, 1111111100000000, 11111111111111110, 111111110999889000, 1111111111111111110, 11111111109999998900, 111111111111109999890

Offset

1,2

Links

Table of n, a(n) for n=1..21.

N. J. A. Sloane, Transforms

Eric Weisstein's World of Mathematics, Repunit

Formula

G.f.: Sum_{n>=1} a(n)*x^n/(1 - x^n) = x/((1 - x)*(1 - 10*x)).

Dirichlet g.f.: (PolyLog(s,10) - zeta(s))/(9*zeta(s)), where PolyLog() is the polylogarithm function.

a(n) = Sum_{d|n} mu(n/d)*(10^d - 1)/9, where mu() is the Moebius function (A008683).

Mathematica

a[n_] := Sum[MoebiusMu[n/d] (10^d - 1)/9, {d, Divisors[n]}]; Array[a, 21]

Prog

(PARI) a(n) = sumdiv(n, d, moebius(n/d)*(10^d-1)/9); \\ Michel Marcus, Nov 05 2018

Crossrefs

Cf. A002275, A008683.

Sequence in context: A290672 A290417 A289405 * A242162 A144099 A102092

Adjacent sequences: A285765 A285766 A285767 * A285769 A285770 A285771

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 25 2017

Status

approved